R. Sbrizzai

A distributed computing approach for real-time transient stability analysis

Power system online dynamic security assessment (DSA) is a challenging computing problem. A key problem in DSA is the analysis of a large number of dynamic stability contingencies every 10-20 minutes using online data. In order to speed up the transient stability analysis, parallel processing has been applied and several results can be found in the literature. In this paper, the authors present a distributed approach for real-time transient stability analysis. Distributed computing is economically attractive providing the processing power of supercomputing at a lower cost. Several distributed software environments like the parallel virtual machine (PVM) allow an effective use of heterogeneous clusters of workstations. Both functional and domain decomposition of the transient stability problem were tested under PVM on a homogeneous cluster of eight DEC ALPHA and on an IBM SP2 machine. Functional decomposition has been obtained by the Shifted-Picard algorithm, whereas domain decomposition has been obtained concurrently running different contingencies on different nodes of the cluster, using the very dishonest Newton algorithm. In order to assess the performance of these approaches, time domain simulations, adopting detailed modeling for synchronous machines, have been carried out on a realistic-sized power network comprising 2583 buses and 511 generators.

A pipelined-in-time parallel algorithm for transient stability analysis (power systems)

A new parallel algorithm for transient stability analysis is presented. An implicit trapezoidal rule is used to discretize the set of algebraic-differential equations which describe the transient stability problem. A parallel-in-time formulation has been adopted. A Newton procedure is used to solve the equations which describe the system at each time step, whereas a Gauss-Seidel algorithm relaxes the solution across the time steps. A Gauss-Seidel-like procedure can be usefully exploited in the parallel processing mode by pipelining the computation through time steps. The parallelism in space of the problem is also exploited. Furthermore, the parallel-in-time formulation is used to change the time steps between iterations by a nested iteration multigrid technique in order to enhance the convergence of the algorithm. The method has the same reliability and model-handling characteristics of typical dishonest Newton-like procedures. Test results on realistic power systems are presented to show the capability and usefulness of the suggested technique. >

Parallel-in-time implementation of transient stability simulations on a transputer network

The most time consuming computer simulation in power system studies is the transient stability analysis. Parallel processing has been applied for time domain simulations of power system transient behavior. In this paper, a parallel implementation of an algorithm based on Shifted-Picard dynamic iterations is presented. The main idea is that a set of nonlinear Differential Algebraic Equations (DAEs), which describes the system, can be solved by the iterative solution of a linear set of DAEs. The time behavior of the linear set of differential equations can be obtained by the evaluation of the convolution integral. In the parallel-in-time implementation of the proposed algorithm, each processor is devoted to the evaluation of the complete set of variables relative to each time step. The quadrature formula, adopted for the integral evaluation, can be easily parallelized by using a number of processors equal to the number of time steps. The algorithm, implemented on a transputer network with 32 Inmos T800/20 adopting a uni-directional ring topology, has been tested on standard power systems. >

A qualitative approach to the transient stability analysis [of power systems]

With the growing stress on todays power systems, there is a urgent need for implementing online dynamic security assessment (DSA). Among the functions of DSA, the most time-consuming function is the dynamic contingency analysis. In this paper, it has been assumed that during this analysis, one is not interested in obtaining trajectories with a very high accuracy but is primarily interested in a qualitative answer to the question: is the power system stable or not? Subsequently, only unstable or marginally stable cases have to be considered for more detailed analyses and preventive control. This idea is applied to parallel-in-time algorithms for transient stability analysis in order to stop the simulation as soon as the stability is detected by the condition of potential energy boundary surface (PEBS) crossing. The effectiveness of the approach has been validated on the New England test system and a realistic-sized network with 662 buses. An implementation on the nCUBE multiprocessor of a particular parallel-in-time algorithm allows the speed up derived from the proposed approach to be assessed.

A simulation tool for studying the day-ahead energy market: the case of Italy

Many challenging issues arise in the newly deregulated competitive electric power markets worldwide. Instead of centralized decision-making in a monopolistic environment, as in the past, many parties with different goals are now involved and competing in the market. Key questions to address include how to predict load and market clearing price (MCP). In this paper a simulation tool for investigating the wholesale energy market in a compulsory power exchange/ISO environment is proposed. For each generator (customer) a multi-stage nondecreasing (nonincreasing) bidding curve is considered, based on an appropriate set of quantity/price pairs. The proposed approach allows the analysis of several crucial aspects which may significantly influence MCP, profits and market shares. Using published and estimated data, the simulation tool is applied to investigate the main features of the Italian wholesale energy market that involves five main companies, represented by a specific set of generation technologies.

A tracking time domain simulator for real-time transient stability analysis

Real-time power system transient stability analysis requires the analysis of hundreds of contingencies in terms of minutes using online data from state estimation. The final objective is to present timely information about transfer limits and stability margins and eventually implement corrective actions. In this paper, the authors assume that the dynamic contingency analysis (DCA) has to be repeated every 15 minutes. During this period of time, the loading and configuration conditions of the system change significantly but not drastically. They verify that the set of the relevant contingencies remains almost the same in the time interval comprised between two cycles of the functions associated to dynamic security analysis (DSA). Parallel-in-time formulated algorithms can be used in tracking the load conditions in real-time adopting as initial guess for the simulation of each contingency, the trajectories obtained for the same contingency at the previous cycle of DSA functions (that is the ones calculated in the previous 15 minutes). In this way, the information obtained in a previous cycle of DCA is not lost completely as in step-by-step algorithms. The feasibility of the approach has been tested on the Italian 380-220kV transmission system operated by ENEL. A parallel implementation of the approach on a nCUBE multiprocessor is reported.

Enhancement of interconnected power system stability using a control strategy involving static phase shifters

Abstract The static phase shifting transformer is one of the potential options of the recently proposed FACTS (flexible AC transmission systems). Promising results have been obtained for enhancing the small-disturbance and the transient stability of interconnected power systems. In this paper, the important concept of involving in the same control strategy both generating units and static phase shifters has been considered. A systematic procedure for designing co-ordinated and decentralized controllers of these components is provided to assure a satisfactory dynamic performance of an interconnected power system under both small and large perturbations. The approach uses optimal control theory as a basis for the co-ordination of static phase shifter and governor controllers. A suboptimal decentralized control scheme is derived from the designed optimal controller by using a ‘minimum norm’ nearness criterion. The resulting feedback control signals for each generating unit and for each phase shifter is expressed in terms of measurable and local variables only. Test results show the effectiveness of the proposed control strategy and the usefulness of control actions on static phase shifters.

Online voltage stability assessment of load centers by using neural networks

This paper presents a neural network based method for evaluating online voltage stability conditions for a selected load center of an electric power system. Starting with a dynamic model of the system, a suitable index is defined to evaluate the proximity of the power network to voltage collapse. Then, a three-layer feedforward neural network is trained to give, as output to a prespecified set of inputs, the expected value of the voltage stability index. For this purpose, two different neural network architectures are proposed. The error back-propagation algorithm is used in this paper to train the chosen neural network structure. Moreover, it is shown that a good estimate of the real power margin of the selected load center can also be obtained using the value of the output of the designed neural network. To demonstrate the effectiveness of the proposed neural network based approach for voltage stability monitoring, a sample power system is considered. Test results show that neural networks can yield, in real time, an accurate assessment of voltage stability conditions.

Coordination of active and reactive distributed resources in a smart grid

The authors present a methodology for assessing centralized control of active and reactive distributed resources in a smart distribution grid. The methodology is based on three-phase optimal power flow and is able to deal properly with unbalanced conditions and both single-phase and three-phase control resources. Single-phase resources that can be exploited by means of this approach are domestic loads, photovoltaic and distributed micro-generation. The methodology is developed on an open-source simulating environment and tested on the IEEE 123-bus Radial Distribution Feeder test case.

Structural approach for the identification of power network dynamic equivalents

A new method for deriving minimum-order dynamic equivalents of power networks is developed. The approach starts with a linearized model in polynomial matrix form of the external power network, seen from its boundary nodes with the study system. Then, the concept of structural dynamic equivalent is introduced as a generalized definition of equivalent related to the order reduction that may occur when deriving the transfer function matrix of the external system and due to pole-zero cancellations. In this case, necessary and sufficient conditions are given for determining systematically the existence of structural equivalents of external systems, their order and exact mathematical representation. Furthermore, the above-mentioned theoretical results are used to develop an algorithm for constructing approximate reduced models, called nearly structural dynamic equivalents, which takes into account the more realistic event of near pole-zero cancellation. Indications about the error bounds of the approximate mode...